Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
long long a, b, n;
int main() {
  scanf("%lld", &n);
  n <<= 1ll;
  for (register int i = 1; i <= n; i++) {
    long long tmp = n - i * (i + 1);
    if (tmp < 0) break;
    long long l = 1, r = n;
    while (l < r) {
      long long mid = l + r >> 1;
      if (mid * (mid + 1) == tmp) {
        printf("YES\n");
        return 0;
      }
      if (mid * (mid + 1) > tmp)
        r = mid;
      else
        l = mid + 1;
    }
    if (l == tmp) {
      printf("YES\n");
      return 0;
    }
  }
  printf("NO\n");
  return 0;
}